Overview

In this performance assessment, students will be asked to use volume to solve real world problems. Specifically, students will be asked to find the best-sized moving truck for their family. They will be given the dimensions of each truck, and all the boxes that will be used. Students will have to calculate the volume of each truck and then the volume of each size box. 

Then, they will need to consider how many boxes of each size will be used. They will need to decide which truck to order based on the volume of the boxes. Students will need to justify their answers with reasoning and calculations. 

This assessment might be used after a unit on finding the volume of rectangular prisms. 

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Details

Big Ideas & Competencies

Big Ideas Competencies

D. Geometric Reasoning

Students can collect and organize data to interpret, model, and investigate issues connected to their communities, lived experiences, and cultural identities.

Solving Measurement Problems 1

Students solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

NOTE ABOUT ASSESSMENT RUBRICS

Below are analytic teacher rubrics. The column on the left shows the dimension that is being measured in the student’s performance. The levels across the top row indicate the performance level in the dimensions. Occasionally all dimensions and performance levels are exemplified by multiple students in a single recording.

Teacher Rubric

Dimensions Not Yet Meeting Expectations Meeting Expectations Exceeding Expectations

Concepts and Procedures
  • Applies some appropriate mathematical processes and/or strategies demonstrating partial understanding of the required concepts and procedures.
  • Calculation errors are present.
  • Solutions may be incomplete, failing to address some of the mathematical components presented in the task.
  • Applies appropriate mathematical processes and strategies demonstrating complete understanding of the required concepts and procedures.
  • Few and minor calculation errors, if any.
  • Solutions are complete and address all mathematical components presented in the task. 
  • Applies appropriate mathematical processes and strategies demonstrating sophisticated understanding of the required concepts and procedures.
  • Uses the most efficient approach to solve the problem.
  • No calculation errors.
  • Solutions completely address all mathematical components presented in the task and demonstrate advanced mathematical fluency, if applicable.

Reasoning and Explaining
  • Attempts to explain the solution(s) to the task and may provide an incomplete justification for the conclusion(s).
  • Uses some, but limited, mathematical terminology and/or notation.
  • Appropriately explains the solution(s) so that the reader does not have to infer how the task was completed.
  • Justifies the conclusion(s) appropriately at multiple decision points.
  • Uses accurate and appropriate mathematical terminology and notation.
  • Clearly and effectively communicates the solution(s) to convey advanced conceptual understanding of the mathematical content.
  • Justifies the conclusion(s) effectively at multiple decision points and may evaluate the efficiency or adequacy of differing approaches.
  • Uses precise and sophisticated mathematical terminology and notation.

Modeling and Using Tools
  • Attempts to use an appropriate representation to model the mathematical concepts or relationships, but the model contains inaccuracies or is incomplete, and/or analyzes and interprets a math model in a limited way.
  • Selects tools and applies with partial accuracy.
  • Uses accurate representations to correctly model the mathematical concepts or relationships, and/or accurately analyzes and interprets a math model.
  • Uses an appropriate tool to solve a problem.
  • Uses an accurate and effective representation to clearly model the mathematical concepts or relationships, and/or accurately analyzes and interprets a math model.
  • Uses an appropriate tool to solve a problem and is able to justify the tool selection.

Seeing Structure and Generalizing
  • Identifies some patterns, structure, and/or repeated calculation in math problems, but applies them incorrectly or in a limited way to solve the problem more efficiently.
  • Identifies patterns, structure, and/or repeated calculations in math problems and uses that information to solve part of the problem more efficiently. 
  • Identifies patterns, structure, and/or repeated calculations in math problems and uses that information to solve problems more efficiently or explain why a shortcut works.

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